//
// Created by hitfy on 2018/4/22.
//参考：https://www.cnblogs.com/TenosDoIt/p/4024413.html
//

#ifndef ALGORITHM_TRIANGLE_H
#define ALGORITHM_TRIANGLE_H
#include<string>
#include<sstream>
#include<fstream>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<algorithm>
#include<ctime>
#include<unordered_map>
#include<map>
#include<typeinfo>
#include<cmath>
#include<ctime>
#include<climits>
using namespace std;

//类定义：二维向量
class Vector2d
{
public:
    double x_;
    double y_;

public:
    Vector2d(double x, double y):x_(x), y_(y){}
    Vector2d():x_(0), y_(0){}

    //二维向量叉乘, 叉乘的结果其实是向量，方向垂直于两个向量组成的平面，这里我们只需要其大小和方向
    double CrossProduct(const Vector2d vec)
    {
        return x_*vec.y_ - y_*vec.x_;
    }

    //二维向量点积
    double DotProduct(const Vector2d vec)
    {
        return x_ * vec.x_ + y_ * vec.y_;
    }

    //二维向量减法
    Vector2d Minus(const Vector2d vec) const
    {
        return Vector2d(x_ - vec.x_, y_ - vec.y_);
    }

    //判断点M,N是否在直线AB的同一侧
    static bool IsPointAtSameSideOfLine(const Vector2d &pointM, const Vector2d &pointN,
                                        const Vector2d &pointA, const Vector2d &pointB)
    {
        Vector2d AB = pointB.Minus(pointA);
        Vector2d AM = pointM.Minus(pointA);
        Vector2d AN = pointN.Minus(pointA);

        //等于0时表示某个点在直线上
        return AB.CrossProduct(AM) * AB.CrossProduct(AN) >= 0;
    }
};

//三角形类
class Triangle
{
private:
    Vector2d pointA_, pointB_, pointC_;

public:
    Triangle(Vector2d point1, Vector2d point2, Vector2d point3)
            :pointA_(point1), pointB_(point2), pointC_(point3)
    {
        //todo 判断三点是否共线
    }

    //计算三角形面积
    double ComputeTriangleArea()
    {
        //依据两个向量的叉乘来计算，可参考http://blog.csdn.net/zxj1988/article/details/6260576
        Vector2d AB = pointB_.Minus(pointA_);
        Vector2d BC = pointC_.Minus(pointB_);
        return fabs(AB.CrossProduct(BC) / 2.0);
    }

    bool IsPointInTriangle1(const Vector2d pointP)
    {
        double area_ABC = ComputeTriangleArea();
        double area_PAB = Triangle(pointP, pointA_, pointB_).ComputeTriangleArea();
        double area_PAC = Triangle(pointP, pointA_, pointC_).ComputeTriangleArea();
        double area_PBC = Triangle(pointP, pointB_, pointC_).ComputeTriangleArea();

        if(fabs(area_PAB + area_PBC + area_PAC - area_ABC) < 0.000001)
            return true;
        else return false;
    }

    bool IsPointInTriangle2(const Vector2d pointP)
    {
        return Vector2d::IsPointAtSameSideOfLine(pointP, pointA_, pointB_, pointC_) &&
               Vector2d::IsPointAtSameSideOfLine(pointP, pointB_, pointA_, pointC_) &&
               Vector2d::IsPointAtSameSideOfLine(pointP, pointC_, pointA_, pointB_);
    }

    bool IsPointInTriangle3(const Vector2d pointP)
    {
        Vector2d AB = pointB_.Minus(pointA_);
        Vector2d AC = pointC_.Minus(pointA_);
        Vector2d AP = pointP.Minus(pointA_);
        double dot_ac_ac = AC.DotProduct(AC);
        double dot_ac_ab = AC.DotProduct(AB);
        double dot_ac_ap = AC.DotProduct(AP);
        double dot_ab_ab = AB.DotProduct(AB);
        double dot_ab_ap = AB.DotProduct(AP);

        double tmp = 1.0 / (dot_ac_ac * dot_ab_ab - dot_ac_ab * dot_ac_ab);

        double u = (dot_ab_ab * dot_ac_ap - dot_ac_ab * dot_ab_ap) * tmp;
        if(u < 0 || u > 1)
            return false;
        double v = (dot_ac_ac * dot_ab_ap - dot_ac_ab * dot_ac_ap) * tmp;
        if(v < 0 || v > 1)
            return false;

        return u + v <= 1;
    }

    bool IsPointInTriangle4(const Vector2d pointP)
    {
        Vector2d PA = pointA_.Minus(pointP);
        Vector2d PB = pointB_.Minus(pointP);
        Vector2d PC = pointC_.Minus(pointP);
        double t1 = PA.CrossProduct(PB);
        double t2 = PB.CrossProduct(PC);
        double t3 = PC.CrossProduct(PA);
        return t1*t2 >= 0 && t1*t3 >= 0;
    }
};

#endif //ALGORITHM_TRIANGLE_H
